Hawaii government leaders received a personal invitation Monday to apply for a record pool of federal grant funding for combating homelessness.

U.S. Housing and Urban Development Secretary Marcia L. Fudge, who wrapped up a two-day visit to Hawaii on Monday, encouraged local government leaders, developers, nonprofits and others to compete for a share of about $3.1 billion to be made available soon under the agency’s Continuum of Care program.

Fudge announced the funding opportunity in HUD’s downtown Honolulu office surrounded by Gov. Josh Green, three of Hawaii’s four representatives in Congress, Hawaii island Mayor Mitch Roth and media.

“We are hopeful that Hawaii and the locals here will apply for those resources,” she said. “Because what we know is that Hawaii is the most expensive state to live in.”

Fudge also said Hawaii has a severely rent-­burdened population and a homelessness problem that affects Native Hawaiians to a high degree.

In a written news release, HUD said Native Hawaiians and Pacific Islanders have the highest per-capita rate of homelessness at 121 per 10,000 people.

The agency said the $3.1 billion being made available represents the largest single-year investment in its Continuum of Care program. A formal notice about the funding opportunity is to be issued soon. Awards will be made based on competitive merits of proposals from across the nation.

Green said there certainly will be applications for a share of the funding to benefit Hawaii.

“We are trying to attack the problem of housing on every front, which is why we’re so grateful to have allies in federal government,” he said.

Hawaii’s congressional representatives at the event — Sen. Mazie Hiro­no and Reps. Ed Case and Jill Tokuda — expressed appreciation and encouragement for the grant opportunity to help address homelessness in the state.

“I’m really grateful to have Secretary Fudge here,” Hirono said. “We’re all going to be working together to maximize the resources that are being provided.”

Case said Hawaii’s strength lies in providing collaborative local government and community bids for grants.

“The federal government likes to see creative, innovating, inclusive solutions to problems … so that’s really where I think our strength lies,” he said.

Tokuda said, “Grants like this are going to allow all our counties and our private partners out there to be very creative, very innovative in looking at ways that are going to help address the housing shortages that exist on all of our islands.”

Applicants can include state agencies, county governments, nonprofits and even developers through public-private partnerships.

Fudge met with some developers during her visit to Hawaii, and she said they want to build more affordable housing.

The HUD leader also visited the state Department of Hawaiian Home Lands on Monday after stopping Sunday to see two Honolulu affordable-­housing projects, Hale Kewalo, a low-­income rental midrise in Kakaako, and a Makiki property operated by Gregory House, a nonprofit that offers housing and program serv­ices primarily for people with HIV.